Notice or Wonder in Math.

 I've been attending a series of webinars that focus on using "What do you notice?" and What do you wonder"? as a way to hook students and to get them to think.  The activity does not have any "right" answers but they open up the way to thinking.

One reason for using this routine regularly is because it helps students develop the persistence they need to solve problems.  If used to introduce a situation or concept, it allows students a chance to pique their curiosity and learn more about the context of the problem.

In addition, this routine gives them time to think about which strategy or strategies could be used to solve the problem while giving them the opportunity to see the whole picture.  Furthermore, it can help students build self confidence, reflection, and the realization that it is possible to solve the problem using a variety of ways.

One nice thing about using the notice and wonder routine is that it encourages students to brainstorm ideas which can help them get started because they are exploring the problem before they actually start.  It also helps students slow down to check out the details, and think about the actual problem rather than rushing through it.  Furthermore, it helps them see the math in a situation where the math may not be as visible as it might be in a problem.

The nice thing about the notice and wonder routine is that it can be used to open a lesson on a new concept, it could be used as a stand alone routine, or it can be spread over a couple of days so the routine begins on the first day and finishes up on the second or third day and can be used as the warmup.  When used regularly, it helps establish a safe environment.

To implement this routine, begin by showing students a situation, word problem with the question removed, a visual representation of a math concept, a set of data, or a graph and ask the students to write down thoughts on what they notice.  The next step is to ask students to share their observations but some students do not like sharing verbally. I have seen it suggested that this be done using a program that allows anonymity for the students so they can express their thoughts without fear or ask students to provide their answers on a slide, doc or post it note app.

Once they've shared their notices, ask them to think about what they wonder for a few minutes.  At the end, ask them to share their questions with each other, either aloud or via slides or a doc.  During this process, do not comment on anything in terms of correctness, do not ask for clarification, restating, or even praising them.  You only want to write down their thoughts and questions.  Use this information to determine where to go next in the lesson.

Next time, I'll be talking a bit more about using photos and such from the regular world where math may not be as visible for notice and wonder.  Let me know what you think, I'd love to hear.  Have a great day.